#include using namespace std; struct frac{ //最終的に分子分母64bitに収まる計算のみ. public: long long n,d; frac() : n(0),d(1){} frac(long long v) : n(v),d(1) {} frac(long long a,long long b,bool redu = true){ assert(b != 0); if(redu) reduce(a,b); n = a,d = b; } private: long long gcd(long long a,long long b){ if(a%b == 0) return b; return gcd(b,a%b); } long long gcd128(long long a,long long b){ //絶対値gcd128. if(b == 0) return abs(a); return gcd(abs(a),abs(b)); } void reduce(long long &a,long long &b){ //約分. if(b < 0) a = -a,b = -b; long long div = gcd128(a,b); a /= div; b /= div; } public: //計算量 O(logmax(d,b.d)). friend frac operator+(const frac &b){return b;} friend frac operator-(const frac &b){return frac(-b.n,b.d,false);} friend frac operator+(const frac &a,const frac &b){ return frac((long long)a.n*b.d+(long long)b.n*a.d,(long long)a.d*b.d); } friend frac operator-(const frac &a,const frac &b){ return frac((long long)a.n*b.d-(long long)b.n*a.d,(long long)a.d*b.d); } friend frac operator*(const frac &a,const frac &b){ long long g1 = std::gcd(a.n,b.d),g2 = std::gcd(a.d,b.n); return frac((a.n/g1)*(b.n/g2),(a.d/g2)*(b.d/g1),false); } friend frac operator/(const frac &a,const frac &b){ assert(b.n != 0); long long g1 = std::gcd(a.n,b.n),g2 = std::gcd(a.d,b.d); if(b.n < 0) return frac((-a.n/g1)*(b.d/g2),(a.d/g2)*(-b.n/g1)); else return frac((a.n/g1)*(b.d/g2),(a.d/g2)*(b.n/g1)); } friend bool operator==(const frac &a,const frac &b){return a.n==b.n && a.d==b.d;} friend bool operator!=(const frac &a,const frac &b){return a.n!=b.n || a.d!=b.d;} friend bool operator>(const frac &a,const frac &b){return (long long)a.n*b.d > (long long)b.n*a.d;} friend bool operator>=(const frac &a,const frac &b){return (long long)a.n*b.d >= (long long)b.n*a.d;} friend bool operator<(const frac &a,const frac &b){return (long long)a.n*b.d < (long long)b.n*a.d;} friend bool operator<=(const frac &a,const frac &b){return (long long)a.n*b.d <= (long long)b.n*a.d;} frac &operator=(const frac &b) = default; frac operator+=(const frac &b){return *this=*this+b;} frac operator-=(const frac &b){return *this=*this-b;} frac operator*=(const frac &b){return *this=*this*b;} frac operator/=(const frac &b){return *this=*this/b;} frac operator++(int){*this += frac(1); return *this;} frac operator--(int){*this -= frac(1); return *this;} double decimal(){return (n+0.0)/d;} long double decimall(){return ((long double)n)/d;} long long num(){return n;} long long den(){return d;} long long floor(){return n<0?(n+1)/d-1:n/d;} long long ceil(){return n>0?(n-1)/d+1:n/d;} frac inv(){return frac(n>=0?d:-d,n>=0?n:-n,false);} }; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int K,N; cin >> K >> N; vector<__int128_t> fac(K+1); fac.at(0) = 1; for(int i=1; i<=K; i++) fac.at(i) = fac.at(i-1)*i; vector mindec(K+1); for(int i=1; i<=K; i++) mindec.at(i) = frac(i,N); long long inf = 1000000000; vector> dp(K+1); dp.at(0)[inf+1] += fac.at(K); for(int i=1; i<=N; i++){ frac dec(1,i); for(int k=K-1; k>=0; k--){ for(auto &[ke,v] : dp.at(k)){ frac now(ke/inf,ke%inf); for(int l=1; l<=K-k; l++){ now -= dec; if(now < 0 || now.d > 20000) break; if(now-mindec.at(K-(k+l)) < 0) break; dp.at(k+l)[now.n*inf+now.d] += v/fac.at(l); } } } } cout << (long long)dp.at(K)[1] << endl; }